This invention relates generally to magnetic resonance spectroscopy, and more particularly the invention relates to multidimensional NMR spectroscopy using switched acquisition time (SWAT) gradients for detecting multiple coherence transfer pathways following a single magnetic excitation sequence.
Nuclear magnetic resonance (NMR) spectroscopy is a method that is used to study the structure and dynamics of molecules. It is completely non-invasive and does not involve ionizing radiation. In very general terms, nuclear magnetic moments are excited at specific spin precession frequencies which are proportional to the local magnetic field. The radio-frequency signals resulting from the precession of these spins are received using pickup coils.
A general description of the principles of NMR is given by Ernst et al. in Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford 1987.
Briefly, a strong static magnetic field is employed to line up atoms whose nuclei have an odd number of protons and/or neutrons, that is, have spin angular momentum and a magnetic dipole moment. A second, rf, magnetic field, applied as a pulse transverse to the static magnetic field (B.sub.0), is then used to pump energy into these nuclei, causing them to process relative to the static field (B.sub.0), by a fixed tip angle for example, 90.degree. or 180.degree.. After excitation the nuclei gradually return to alignment with the static field and give up the energy in the form of weak but detectable free induction decay (FID). These FID signals are used by a computer to produce spectra.
The excitation frequency is defined by the Larmor relationship which states that the angular frequency .omega..sub.0, of the procession of the nuclei is the product of the magnetic field, B.sub.0, and the so-called magnetogyric ratio, .gamma., a fundamental physical constant for each nuclear species: EQU .omega..sub.0 =B.sub.0.multidot..gamma.
The angle of nuclear spin tip in response to an rf pulse excitation is proportional to the integral of the pulse over time.
Multidimensional NMR spectroscopy provides a method for studying the structure, dynamics, and reactions of molecules. The interaction between the magnetic moments of atomic nuclei and magnetic fields are a function of two or more frequency variables providing a signal function S(.omega..sub.1, .omega..sub.2, .omega..sub.3...) which contains detailed chemical information. The pulse sequence of a multidimensional NMR procedure includes preparation of the nuclear spins by interaction of the nuclear magnetic moments and applied magnetic fields, evolution of the magnetic moments over a time (t.sub.1), magnetization transfer, between nuclei (e.g. hydrogen to carbon), and detection over a time (t.sub.2). Signals from various coherence transfer pathways can be detected using a sequence of rf and gradient pulses for selection. Heretofore, a signal from a single pathway has been sampled at a plurality of points in time following excitation and evolution. The sampling of a plurality of coherence transfer pathways has required sequential rf excitations with a unique magnetic gradient sequence for each pathway, thus necessitating multiple acquisitions. Fourier transformation is utilized to analyze the detector signals.
In general, the effect of a pulsed magnetic field gradient on the nuclear spins can be understood by describing the state of the spin system in terms of density operators. The density operator .rho.(t) of the spin system at any time t can be classified according to the various coherence orders: EQU .rho.(t)=.rho..SIGMA..rho..sup..rho. (t), [1]
where p represents the coherence order. The Hamiltonian of the system during the gradient pulse is predominantly from Zeeman contributions. Classification of the density operator into its various components is convenient, since the effect of a field gradient pulse of duration .tau. can be written as ##EQU1## where .rho.(t-) and (t+) are used to label the density operator before and after the gradient pulse, and Fz is the z component of the total angular momentum. The Zeeman fields experienced by the various spins in the sample vary according to their spatial coordinates. It can be seen from equation [2] that the gradient pulse introduces a complex phase factor into the density operator component. This phase factor depends on the coherence order of the component and on the area of the gradient pulse. Essentially, the effect of the gradient pulse is to defocus the coherence by a controlled amount. Each of the coherence pathways can be thought to be "coherence order labeled" by the gradients. Selection of a particular pathway is then accomplished by applying a rephasing gradient pulse integral of .omega..sup.R.sub.Z (r) .tau..sup.R, which transforms the density operator, described by K.SIGMA.C.sub.k.rho..sup.(-1)exp{-i.phi..sub.k } where k denotes a particular coherence pathway, .phi..sub.k is the phase dispersal, c.sub.k denotes all of the time dependence and .rho..sup.(-1) denotes the observable component corresponding to p=-1. The refocusing gradient transforms the density operator as shown: EQU exp{i.omega..sup.R.sub.Z (r)F.sub.z.tau..sup.R} ##EQU2## where 1 is the desired pathway. The first term on the right hand side of equation [3] corresponds to the pathway which has been exactly refocused and is hence observable, since EQU .phi..sub.80=-.omega..sup.R.sub.Z (r).tau..sup.R [ 4]
The second term denotes all the other pathways which are still defocused and are not observable.
Equation [2] describes the central property of all coherence transfer selection schemes. In conventional NMR, each coherence component accumulates phase factors during the various cycles of the phase cycle scheme. The receiver phase cycle is then determined such that only the desired pathway yields a signal. In an experiment where pulsed gradients are used, each of the gradient pulses contributes to the cumulative phase factors of the various coherence components. The desired pathway can then be selected by choosing the area of the gradient prior to data acquisition, so that only the desired signal component is refocused. A major feature of gradient selection of coherence pathways is that the selection is accomplished in a single acquisition, unlike rf phase cycling, where multiple acquisitions are required. The major limitation of conventional gradient selection has been the loss of all but a single pathway, and hence usually the loss of the square root of 2 in signal to noise and loss of the potential for pure-absorption 2D line shapes.